vp_wiz wrote: "For example, generally speaking, betting below Kelly is no more advantageous to bankroll growth than betting above Kelly. So, it's difficult for me to understand why your scheme (that sets a Kelly bet as a upper threshold) stands out as optimal in this respect. "
Sometimes there are two betsizes that yield the same average bankroll growth, but why would you take the higher betsize? It's possible there is a valid bet on the dark side that has a higher growth than the valid bet on the good side, but you're playing with fire. In the real world there are Rumsfeldian unknown unknows, and those are going to get you into trouble on the dark side. On one side of Kelly, the good side, there is always bankroll growth and growth is proportional to risk, the more risk you take, the more growth you get in return. You make a mistake and take a bit more risk than you wanted to, at least you get a better return for taking that risk, up to a point. Not true on the other side, the dark side, there the more risk you take the less growth you get and eventually the growth even turns negative. On this side there be dragons. Actually, a better analogy would be a black hole. The good side has some built in stability, the bad side is unstable and eventually turns ugly, faster than your expecting, that black hole will suck you in. Sure, if you're really really good and really really know what you're doing, you could play around on that dark side, but, as your mother told you, it's not safe, you could shoot your eye out kid. I'd recommend Poundstone's book "Fortune's Formula" for a non mathematical discussion of this topic and its real world implications.
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Posted by: nightoftheiguana2000@yahoo.com
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